覆盖、对应和非交换几何(英文)

本书是一部英文版的数学专著。本书内容相当艰深且小众，估计只有少数研究者才会感兴趣.但由于雅可比猜想是一个历史感颇强的大猜想且至今无人解决，所以笔者相信一定会有人从收藏心态购买之。

   1.Introduction

Chapter 1.Graphs Category and Three-manifolds as correspondences

1.Three-manifolds as correspondences

2.Composition ofcorrespondencas

3.Representations and compositions of correspondences

4.Semigroupoids and additive categories

5.Categories of graphs and correspondences

6.Convolution algebra and time evolution

7.Equivalence of correspondences

8.Convolution algebras and 2-semigroupoids

9.Vertical and horizontal time evolutions

10.Vertical time evolution: Hattie-Hawking gravity

11.Vertical time evolution: gauge moduli and index theory

12.Horizontal time evolution: bivariant Chern character

13.Noncommutative spaces and spectral correspondences

Chapter 2.Knots, Khovanov Homology

1.Introduction

2.From graphs to knots

3.Khovanov Homology

4.Knots and Links Cobordism Groups

5.Graphs and cobordisms

6.Homology theories for embedded graphs

7.Questions and Future Work

Appendix A.

1.Branched Covering

2.Filtration

3.Knot and link

4.Topological Quantum Field Theory

5.2-Category

6.Group Rings

7.Creation and annihilation operators

8.A quick introduction to Dirac operators

9.Concepts of Cyclic Cohomology

Appendix.Bibliography

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